Combined survey sampling inference: weighing Basu's elephants
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London u.a.
Arnold
2002
|
| Ausgabe: | 1. publ. in Great Britain |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 316 S. |
| ISBN: | 0340692294 |
Internformat
MARC
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| 245 | 1 | 0 | |a Combined survey sampling inference |b weighing Basu's elephants |c Ken Brewer |
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| 264 | 1 | |a London u.a. |b Arnold |c 2002 | |
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| 650 | 4 | |a Inference | |
| 650 | 4 | |a Sampling (Statistics) | |
| 650 | 4 | |a Inference | |
| 650 | 4 | |a Sampling (Statistics) | |
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Datensatz im Suchindex
| _version_ | 1804129574697566208 |
|---|---|
| adam_text | Contents
Acknowledgements xi
Prologue: Hints on How to Read this Book 1
1 Simple Random Sampling with Equal Weights 4
Narrator s Introduction 4
Simple Random Sampling without Replacement 8
Simple Random Sampling with Replacement 14
Simple Random Sampling: the Prediction Based Theory 18
An Excursus on Independence, Exchangeability and
Non informative Sampling 22
Prediction Based Theory (Continued) 23
Summary 26
Exercises 27
2 Stratification and Poststratification 29
Stratifying the Population 29
Poststratified Estimation 29
Designing a Stratified Sample 34
Summary 37
Exercises 38
3 Ratio Estimation (Design Based) 40
Finding a Supplementary Variable 40
The Classical Ratio Estimator under Design Based Inference 41
Exact Bias of Ratio Estimator 43
Asymptotic Approximations to the Relative Design Bias
and Relative Design Variance of the Ratio Estimator 44
Asymptotic Approximations to the Actual Design Bias and
Actual Design Variance of the Ratio Estimator 46
Numerical Results 48
Across Stratum (or Combined) Ratio Estimation 52
Exercises 57
vi Contents
4 Ratio Estimators for Unequal Probability Samples 60
Facing the Dilemma 60
The Lahiri Midzuno Unbiased Ratio Estimator 60
The Horvitz Thompson and Hansen Hurwitz Estimators of Total 63
Poisson Sampling 74
Exercises 79
5 Ratio Estimation (Prediction Based) 80
Understanding the Difference 80
The Ratio Prediction Model 83
Exercises 93
6 The Reporting 95
Report to Supervisor 95
Draft of a Report for the Circus Owner 98
Comments from Supervisor 98
Action Consequential on Supervisor s Comments 99
Randomization Based and Prediction Based Sampling
Inferences are Complementary 101
More about the Background to Our Assignment 104
7 The Simple Regression Estimator and Synthetic Estimation 107
Report for Supervisor: Introduction 107
Circumstances Favourable for Simple Regression Estimation 108
Questionable Reasons for Using Simple Regression Estimation 109
Properties of the Simple Regression Estimator 112
Some Empirical Evidence 119
Summary 121
Conclusions 121
Response from Supervisor 121
Exercises 121
8 Regression Estimation with More Than One
Supplementary Variable 123
Report for Supervisor: Introduction 123
Combining the Inferences When Using Simple Random
Sampling without Replacement 123
Combining the Inferences When Sampling with
Unequal Probabilities 127
Generalization to p Regressor Variables 128
The Problem of Unacceptably Small Case Weights 133
Design Variance and Anticipated Variance of any Generalized
Regression Estimator 135
Contents vii
Prediction Variance of any Prediction Unbiased Linear Estimator
Based on a Probability Sample 138
Estimation of the Prediction Variances of Individual Sample Units 139
Response from Supervisor 143
Exercises 143
9 Short Cut Variance Estimation for the Horvitz Thompson and
Generalized Regression Estimators 146
Report for Supervisor: Introduction 146
Some Approximate Formulae for the Design Variance of
the Horvitz Thompson Estimator 148
A Model Assisted Check on the Usefulness of the Approximate
Horvitz Thompson Estimator s Design Variance Formulae 154
Sample Estimators of the High Entropy Anticipated
Variance of the Horvitz Thompson Estimator 156
Sample Estimators of the Design Variance of the Horvitz Thompson
Estimator Suitable for Use with Ordered Systematic Sampling 159
Adaptation to Estimating the Design Variance of a
Generalized Regression Estimator 161
Some Empirical Results 163
Response from Supervisor 167
Postscripts 167
Exercises 172
10 Multistage Area Sampling for Household Surveys:
Sampling with Replacement 174
Report for Supervisor: Introduction 174
How a Multistage Equal Probability Sample Can Be Selected 177
Selecting Persons Associated with Dwellings:
Eligibility and Coverage 183
Survey Coverage and Survey Scope 185
The Self Weighting Nature of an Equal Probability
Multistage Sample 186
Estimation Formulae for Multistage Samples 188
Variance Estimation Formulae for Multistage Samples 191
Estimating the Total Variance 196
Estimating the Individual Stages of Variance 197
Optimal Levels of Clustering 199
The Variance Components Reconsidered 199
The Cost Parameters 203
Equations for Optimum Clustering 204
A Quick Fix 205
Acknowledgement from Supervisor 208
Exercises 208
viii Contents
11 Multistage Area Sampling for Household Surveys:
Sampling without Replacement 209
Report for Supervisor: Introduction 209
Selecting a Multistage Equal Probability Sample of Dwellings
without Replacement 209
Estimation Formulae for Multistage Samples Selected
without Replacement 212
Variance Estimation Formulae for Multistage Samples Selected
without Replacement 214
Estimating Y* Using Combined Design Based and
Prediction Based Inference 219
Estimating the Prediction Based, Design Based and
Anticipated Variances of Y* (Totals and Components) 223
Estimation of Variance Using Jackknife, Bootstrap and Other
Resampling Methods 228
Response from Supervisor 229
Exercises 229
12 Multiphase Sampling, Repeated Sampling and Non response 231
Introduction 231
Report on Non response and Related Topics 231
Response from Supervisor 244
Exercises 244
13 Tracking and Rotating Samples 246
Introduction 246
Permanent Random Number Sampling 247
Bernoulli Sampling 247
Poisson Sampling 248
Rotation and Control of a Poisson Sample 248
The Problem with Having a Random Sample Size 251
Estimation and Variance Estimation for a Poisson Sample 252
Two Ways of Viewing the Horvitz Thompson Ratio Estimator 254
Alternatives to Poisson Sampling 256
Response from Supervisor 266
Exercises 266
14 Coping with Extreme Values and Other Unusual Features 268
Report for Supervisor: Introduction 268
Relevant and Recognizable Subsets 268
Stratification and Selection of Atypical Units 270
Spurious Extreme Values 271
Genuine Extreme Values 272
Contents ix
Winsorization 274
Spreading the Estimated Bias Back 278
Summary and Concluding Remarks 280
Response from Supervisor 281
Exercises 282
15 Resampling Methods of Variance Estimation:
the Jackknife and the Bootstrap 283
Report to Supervisor: Introduction 283
Jackknifing the Variance 284
Bootstrapping the Variance 285
Some Semi empirical and Empirical Findings 286
Response from Supervisor 287
Exercise 287
Epilogue: The Most Important Topic Left Out 288
The Other Statistical Inference Controversy 288
Statistical Inference under Tractable Distributions 288
The Inference Problem When the Distributions are Intractable 291
Postscript: Bayesian Methods for Estimation 293
Appendices
A Basu s Original Elephant Fable 297
B The Circus s 50 Indian Elephants 298
C Details of Calculations in the Postscript 299
References 303
Index 310
|
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| id | DE-604.BV014798992 |
| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 0340692294 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010015049 |
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| spelling | Brewer, Ken Verfasser aut Combined survey sampling inference weighing Basu's elephants Ken Brewer 1. publ. in Great Britain London u.a. Arnold 2002 XII, 316 S. txt rdacontent n rdamedia nc rdacarrier Inference Sampling (Statistics) HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010015049&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brewer, Ken Combined survey sampling inference weighing Basu's elephants Inference Sampling (Statistics) |
| title | Combined survey sampling inference weighing Basu's elephants |
| title_auth | Combined survey sampling inference weighing Basu's elephants |
| title_exact_search | Combined survey sampling inference weighing Basu's elephants |
| title_full | Combined survey sampling inference weighing Basu's elephants Ken Brewer |
| title_fullStr | Combined survey sampling inference weighing Basu's elephants Ken Brewer |
| title_full_unstemmed | Combined survey sampling inference weighing Basu's elephants Ken Brewer |
| title_short | Combined survey sampling inference |
| title_sort | combined survey sampling inference weighing basu s elephants |
| title_sub | weighing Basu's elephants |
| topic | Inference Sampling (Statistics) |
| topic_facet | Inference Sampling (Statistics) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010015049&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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